Question 1183754
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The sum of two whole number is 45 and their difference is less than 10. what is the number of possible pair
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<pre>
You are given a system, consisting of one equation and one inequality

    x + y = 45    (1)

    x - y < 10    (2)

where  x  and  y  are whole numbers.


Let solve the problem graphically to make the solution visible.


The figure below shows the line  x + y = 45  (red line)  and line y = x - 10 (green line).


The solution set for the system (1), (2) is the set of integer points on the red line, that are ABOVE the green line.



    {{{drawing(1000, 1000, -10, 50, -10, 50,
            grid(1),

       graph  (1000, 1000, -10, 50, -10, 50,        
              45-x, x-10)
)}}}


                                Plot x + y = 45 (red),  y = x -10 (green)



You can count these points manually.


Their number is  (a)  28, if the zero is admitted for x as a whole number,

             or  (b)  27, if the zero is NOT admitted for x as a whole number.


The set of solutions is  (0,45), (1,44), (2,43), (3,42), . . . , (27,18) in case (a)  (28 pairs)

                     or          (1,44), (2,43), (3,42), . . . , (27,18) in case (b)  (27 pairs)
</pre>

Solved.



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I do not agree with the @greenestamps comment regarding my solution,

as well as I do not agree with his solution.


@greenestamps actually solved another problem, which says


<pre>
    The sum of two whole number is 45 and their <U>distance on the number line</U> is less than 10. 
    What is the number of possible pair ?
</pre>


In my post, I solved the problem CORRECTLY and exactly as it was formulated/worded in the post.